GED Math Practice Test

In the Pythagorean theorem, what type of triangle is being referenced?

1. Equilateral triangle

2. Isosceles triangle

3. Right triangle

4. Scalene triangle

The correct answer is: Equilateral triangle

The Pythagorean theorem specifically pertains to right triangles, which are characterized by having one angle that measures exactly 90 degrees. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This unique relationship is foundational in geometry and allows for the calculation of unknown side lengths when the other two are known. In contrast, the other types of triangles do not have such a relationship defined by the Pythagorean theorem. For example, equilateral triangles have all sides equal and all angles measuring 60 degrees, while isosceles triangles have at least two equal sides but do not necessarily have a right angle. Scalene triangles have sides of different lengths and angles of different measures, which also does not lend itself to the Pythagorean relationship. Hence, the correct association of the theorem is solely with right triangles.